Standard +0.3 This question requires applying the tan addition formula twice, algebraic manipulation to form a quadratic in tan θ, then solving. While it involves multiple steps and careful algebra, it's a standard application of a core P3 technique with no novel insight required. The 'hence solve' structure guides students through the method, making it slightly easier than average.
Use \(\tan(A \pm B)\) formula and obtain an equation in \(\tan\theta\)
M1
Using \(\tan 60° = \sqrt{3}\), obtain a horizontal equation in \(\tan\theta\) in any correct form
A1
Reduce the equation to \(3\tan^2\theta + 4\tan\theta - 1 = 0\), or equivalent
A1
Solve a 3-term quadratic for \(\tan\theta\)
M1
Obtain a correct answer, e.g. \(12.1°\)
A1
Obtain a second correct answer, e.g. \(122.9°\), and no others in the given interval
A1
## Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use $\tan(A \pm B)$ formula and obtain an equation in $\tan\theta$ | M1 | |
| Using $\tan 60° = \sqrt{3}$, obtain a horizontal equation in $\tan\theta$ in any correct form | A1 | |
| Reduce the equation to $3\tan^2\theta + 4\tan\theta - 1 = 0$, or equivalent | A1 | |
| Solve a 3-term quadratic for $\tan\theta$ | M1 | |
| Obtain a correct answer, e.g. $12.1°$ | A1 | |
| Obtain a second correct answer, e.g. $122.9°$, and no others in the given interval | A1 | |
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